The function fx95x32 models the temperature in degrees...

The function F(x) = 9/5x + 32 models the temperature in degrees Fahrenheit, given the temperature, x, in degrees Celsius. Part A Which expression models F^(-1)? 5/9(x - 32) Part B What is the value of F^(-1)(50) and what does it represent? Select from the drop-down lists to correctly complete the sentence. The value is ___ (0, 10, 32, 45.6, 58) and it represents the temperature in degrees ___ (Fahrenheit, Celsius) when the temperature is 50 ___ (Fahrenheit, Celsius).

Transcript

00:01 For this problem, we were given the function f of x equals 9 fits x plus 32, which models the temperature in degrees fahrenheit, given that x is degrees celsius.

00:14 Our task is to find the inverse function, and then find the value of the inverse function, given that we input 50.

00:22 Okay, so let's get started.

00:24 First, we'll find this inverse function.

00:27 I am going to rewrite this function just a little bit before i, go ahead and try to find the inverse.

00:35 So the only thing i'm going to do is instead of f of x, i am going to write y.

00:39 So y equals nine fits x plus 32, just makes things a little easier.

00:49 Now when finding the inverse, pretty much what happens is that your inputs and your outputs basically flip.

00:58 So x become y, ys become x.

01:02 So i'm going to write that here.

01:04 From this here on out, we're going to change all the x's to y's and all the ys to x's.

01:13 So again, we're flipping around the inputs versus outputs.

01:20 And now what we're going to do here is we're going to solve for x.

01:23 Not sell for x, sorry.

01:24 Sell for y.

01:25 Get y by itself on one side of the equation.

01:29 So let me maybe subtract 32 from both sides.

01:35 And then i'll have x minus 32 on the left hand side equals 9 fits.

01:40 Times y.

01:43 And then i want y by itself on one side of the equation.

01:47 So what i can do is i can multiply both sides by the reciprocal nine fits, which is five over nine.

01:56 And you want to do that because if you multiply these two fractions out, when you multiply a fraction with it's reciprocal, it just becomes one.

02:02 So one y is just y.

02:05 So again, i'm multiplying both sides of the equation by five nines.

02:09 And if i'm multiplying both sides of the equation, i want to make sure i'm doing five nines times times the entire left hand side.

02:17 Okay, so now we have this.

02:25 Okay, when i rewrite it again, this time, instead of y, i'm going to use our function notation.

02:33 This here, this expression, actually tells us our inverse function...